General logical databases and programs: Default logic semantics and stratification

AbstractDefault logic is introduced as a well-suited formalism for defining the declarative semantics of deductive databases and logic programs. After presenting, in general, how to use default logic in order to define the meaning of logical databases and logic programs, the class of stratifiable databases and programs is extensively studied in this framework. Finally, the default logic approach to the declarative semantics of logical databases and programs is compared with the other major approaches. This comparison leads to showing some advantages of the default logic approach

Negation by default and unstratifiable logic programs

AbstractThe default approach to the theory of logic programs (and deductive databases) is based on the interpretation of negation by default rules. Default logic is a well-suited formalism to express the Closed World Assumption and to define the declarative semantics of stratifiable logic programs. The case of disjunctive consequences in rules is treated. General logic programs may not have a meaning with respect to default semantics. The contribution of the paper is to exhibit an interesting class of programs having a default semantics, called effectively stratifiable programs. This time, disjunctive consequences are not considered. Effective stratification is a weaker constraint than stratification, local stratification and weak stratification. Besides enlarging the class of stratifiable logic programs, the paper contributes to provide a constructive definition of well-founded models of logic programs. The class of effectively stratifiable logic programs matches the class of programs having a total well-founded model and in general, the default semantics extends the well-founded semantics

An incremental algorithm for generating all minimal models

AbstractThe task of generating minimal models of a knowledge base is at the computational heart of diagnosis systems like truth maintenance systems, and of nonmonotonic systems like autoepistemic logic, default logic, and disjunctive logic programs. Unfortunately, it is NP-hard. In this paper we present a hierarchy of classes of knowledge bases, Ψ1,Ψ2,… , with the following properties: first, Ψ1 is the class of all Horn knowledge bases; second, if a knowledge base T is in Ψk, then T has at most k minimal models, and all of them may be found in time O(lk2), where l is the length of the knowledge base; third, for an arbitrary knowledge base T, we can find the minimum k such that T belongs to Ψk in time polynomial in the size of T; and, last, where K is the class of all knowledge bases, it is the case that ⋃i=1∞Ψi=K, that is, every knowledge base belongs to some class in the hierarchy. The algorithm is incremental, that is, it is capable of generating one model at a time

Achieving tightness in dl-programs

Reviewed by Francisco MartinsIn the field of the combination between description logics and rule-based reasoning systems, dl- programs have proved to be a very successful mechanism. One of their recognized shortcomings, however, is their lack of full tightness: the language constructs that feed data from the logic program have a local effect, leaving the knowledge base essentially unchanged throughout. In this paper, we present a construction that we call lifting, which allows predicates to be fully shared between the two components of a dl-program in a systematic way, and show how lifting can be used to provide intuitive solutions to a number of everyday reasoning problems involving the verification of integrity constraints and the implementation of default rules. This construction preserves consistency of the underlying knowledge base and complexity of the overall system. Furthermore, the resulting semantics of default rules has a natural interpretation under the original Reiter semantics

Semantics of logic programs with explicit negation

After a historical introduction, the bulk of the thesis concerns the study of a declarative semantics for logic programs. The main original contributions are: ² WFSX (Well–Founded Semantics with eXplicit negation), a new semantics for logic programs with explicit negation (i.e. extended logic programs), which compares favourably in its properties with other extant semantics. ² A generic characterization schema that facilitates comparisons among a diversity of semantics of extended logic programs, including WFSX. ² An autoepistemic and a default logic corresponding to WFSX, which solve existing problems of the classical approaches to autoepistemic and default logics, and clarify the meaning of explicit negation in logic programs. ² A framework for defining a spectrum of semantics of extended logic programs based on the abduction of negative hypotheses. This framework allows for the characterization of different levels of scepticism/credulity, consensuality, and argumentation. One of the semantics of abduction coincides with WFSX. ² O–semantics, a semantics that uniquely adds more CWA hypotheses to WFSX. The techniques used for doing so are applicable as well to the well–founded semantics of normal logic programs. ² By introducing explicit negation into logic programs contradiction may appear. I present two approaches for dealing with contradiction, and show their equivalence. One of the approaches consists in avoiding contradiction, and is based on restrictions in the adoption of abductive hypotheses. The other approach consists in removing contradiction, and is based in a transformation of contradictory programs into noncontradictory ones, guided by the reasons for contradiction

Temporal Answer Set Programming

[Abstract] Commonsense temporal reasoning is full of situations that require drawing default conclusions, since we rarely have all the information available. Unfortunately, most modal temporal logics cannot accommodate default reasoning, since they typically deal with a monotonic inference relation. On the other hand, non-monotonic approaches are very expensive and their treatment of time is not so well delimited and studied as in modal logic. Temporal Equilibrium Logic (TEL) is the first non-monotonic temporal logic which fully covers the syntax of some standard modal temporal approach without requiring further constructions. TEL shares the syntax of Linear-time Temporal Logic (LTL) (first proposed by Arthur Prior and later extended by Hans Kamp) which has become one of the simplest, most used and best known temporal logics in Theoretical Computer Science. Although TEL had been already defined, few results were known about its fundamental properties and nothing at all on potential computational methods that could be applied for practical purposes. This situation unfavourably contrasted with the huge body of knowledge available for LTL, both in well-known formal properties and in computing methods with practical implementations. In this thesis we have mostly filled this gap, following a research program that has systematically analysed different essential properties of TEL and, simultaneously, built computational tools for its practical application. As an overall, this thesis collects a corpus of results that constitutes a significant breakthrough in the knowledge about TEL.[Resumen] El razonamiento temporal del sentido común está lleno de situaciones que requieren suponer conclusiones por defecto, puesto que raramente contamos con toda la información disponible. Lamentablemente, la mayoría de lógicas modales temporales no permiten modelar este tipo de razonamiento por defecto debido a que, típicamente, se definen por medio de relaciones de inferencia monótonas. Por el contrario, las aproximaciones no monótonas existentes son típicamente muy costosas pero su manejo del tiempo no está tan bien delimitado como en lógica modal. Temporal Equilibrium Logic (TEL) es la primera lógica temporal no monótona que cubre totalmente la sintaxis de alguna de las lógicas modales tradicionales sin requerir el uso de más construcciones. TEL comparte la sintaxis de Linear-time Temporal Logic (LTL) (formalismo propuesto por Arthur Prior y posteriormente extendido por Hans Kamp), que es una de las lógicas más simples, utilizadas y mejor conocidas en Teoría de la Computación. Aunque TEL había sido definido, muy pocas propiedades eran conocidas, lo que contrastaba con el vasto conocimiento de LTL que está presente en el estado del arte. En esta tesis hemos estudiado diferentes aspectos de TEL, una novedosa combinación de lógica modal temporal y un formalismo no monótono. A grandes rasgos, esta tesis recoge un conjunto de resultados, tanto desde el punto de vista teórico como práctico, que constituye un gran avance en lo relativo al conocimiento sobre TEL.[Resumo] O razoamento do sentido común aplicado ao caso temporal está cheo de situacións que requiren supoñer conclusións por defecto, posto que raramente contamos con toda a información dispoñible. Lamentablemente a maioría de lóxicas modais temporáis non permiten modelar este tipo de razoamento por defecto debido a que, típicamente, están definidas por medio de relacións de inferencia monótonas. Pola contra, as aproximacións non monótonas existentes son moi costosos e o seu tratamento do tempo non está ben tan delimitado nin estudiado como nas lóxicas modais. Temporal Equilibrium Logic (TEL) é a primeira aproximación non monótona que cubre totalmente a sintaxe dalgunha das lóxicas modais traidicionáis sen requerir o uso de máis construccións. TEL comparte a sintaxe de Lineartime Temporal Logic (LTL) (formalismo proposto por Arthur Prior e extendido posteriormente por Hans Kamp), que é considerada unha das lóxicas modais máis simples, utilizadas e coñecidas dentro da Teoría da Computación. Aínda que TEL xa fora definido previamente, moi poucas das súas propiedades eran coñecidas, dato que contrasta co vasto coñecemento de LTL existente no estado da arte. Nesta tese, estudiamos diferentes aspectos de TEL, unha novidosa combinación de lóxica modal temporal e un formalimo non monótono. A grandes rasgos, esta tese recolle un conxunto de resultados, tanto dende o punto de vista teórico como práctico, que constitúe un gran avance no relativo ó coñecemento sobre o formalismo TEL